# Newton's third law to explain lift

sarm2005
Ok so I just read this statement as part of an explanation of list using Newton's 3rd law

"The amazing thing about wings is that because they are flying through air which is a fluid, the top of the wing deflects air down as well as the bottom of the wing."

What I don't understand is how the top of the wing deflects air downwards. Anyone care to explain?

Crazy Tosser
I have no idea what that statement said.

Wings fly because their shape creates overpressure under and underpressure over them.
That's why racing cars have "inverted" wings, to keep them on the ground

http://wings.avkids.com/Book/Animals/Images/wing_diagram.gif [Broken]

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sarm2005
What you just said is an explanation of lift using Bernoulli's principle. Another explanation is using Newton's 3rd law which is what I'm talking about.

Homework Helper
This website does a descent job of explaining it, with a lot of emphasis on Coanda effect, but towards the end of this web site, there's a diagram of a wind blowing over a roof, and although the air downwind of the roof is turbulent, it's also at lower pressure, due to what some call "void" effect: when a solid object passes through a fluid, or when a fluid passes around a solid object, low pressure "voids" are created because the solid object blocks or diverts the fluid flow away from these low pressure areas.

After visiting a large number of web sites, my conclusion is that lift is a combination of Coanda and "void" effects.

http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html [Broken]

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Staff Emeritus
Wings fly because their shape creates overpressure under and underpressure over them.
That's a misapplication of Bernoulli's principle to explain lift. This misapplication is unfortunately used quite widely. The attached diagram is simply incorrect. If the plane is to go up (or even stay level), something else must go down. That something else is air: The wings deflect air downward. Lift results from Newton's third law.

How the bottom side of the wing accomplishes this downward deflection is obvious. How the top of the wing contributes to this deflection at all is a lot less obvious. Moreover, in a good wing, it is the top rather than the bottom that does the bulk of the work in deflecting air downward. The link Jeff Reid posted does a nice job of explaining the Coanda effect.

Mentor
I would say that the sentence you quoted from Crazy Tosser is correct. The application of that sentence (the diagram he linked) is incorrect. The error is that the diagram shows the air straightening out after passing the wing instead of continuing downward as Newton's third law demands.

Also, just a little note - it is quite common for the lower surface of a wing to contribute nothing at all to the lift being generated by that wing.

Homework Helper
Also, just a little note - it is quite common for the lower surface of a wing to contribute nothing at all to the lift being generated by that wing.
Actually this would be rare. Even in the case of flat bottom air foils which are less efficient, but easier to manufacture, than fully cambered airfoils, the aircraft that use them need a signficant angle of attack to fly. I recall an article mentioning that a Cessna would need a speed around 300mph instead of 150mph to fly with the flat bottom airfoil lower surface horizontal, instead of pitched upwards. Most commercial aircraft fly with a significant angle of attack, especially if they are near capacity, getting some amount of lift from the fuselage itself. The pitched up attitude is enough that you can feel it in the seats, and it's clear that the snack or meal carts need their brakes in order to keep from rolling to the back of the aircraft.

For normal air foils, most, but not all, of the lift force comes from above the wing, with a few exceptions like this lifting body prototype:

M2-F2 glider with F104 chase plane:
m2-f2.jpg

M2-F3 rocket powered model (reached a speed of Mach 1.6) with B52:
m2-f3.jpg

mordechai9
First of all, aircraft wings are usually fixed to the body at a slight positive angle. This is referred to as the wing's angle of attack. If you look at an aircraft sitting flat on the runway, with the cockpit facing left, you should be able to see this. The wing is actually turned clockwise a few degrees; the wing is pitched up, even when the aircraft body is flat. They do this because typical airfoil/wing geometries generate lift only when the wing sits at a positive angle of attack. Thus, by affixing the wing to the aircraft in this way, the aircraft will generate lift even when the body is sitting flat on the runway.

Now, imagine the aircraft on the runway again, with the cockpit facing to the left, as before. As the aircraft takes off, the airflow hits the wing, and "attaches" to it as it flows around it, assuming that the wing is properly designed and the flow remains laminar. Laminar flow basically just means that the airflow goes smoothly and continuously around the wing. From this, and considering how we just described the positive pitch of the wing, it's easy to see that the region of flow approaching the wing from the front turns downwards as it follows the shape of the wing. Hence, the top of the wing deflects the air downwards, but it's not like it's the top of the wing acting alone; it's really the entirety of the wing shape and geometric composition.

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Mentor
Actually this would be rare.
I'm not so sure. Here's the data for a 172: http://www.prism.gatech.edu/~gtg635r/Lift-Drag%20Ratio%20Optimization%20of%20Cessna%20172.html [Broken]

Here's a picture of the airfoil: http://www.windmission.dk/workshop/BasicBladeDesign/naca.html [Broken]

It's not flat on the bottom, it's curved, which means that at zero AoA the bottom surface has a negative contribution to the lift. By my calculation, with a .25 CL at 0 AoA, and a cruise weight of 2000 lb, it would need to be flying at 133 mph. Cruise speed for the 172 is 130mph. This is likely by design, as the minimum Cd tends to occur near 0 AoA.

Also: this link appears to show that at 6 degrees AoA, the bottom surface produces roughly zero lift (due to the velocity averaging 1): http://www.mh-aerotools.de/airfoils/velocitydistributions.htm

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Homework Helper
By my calculation, with a .25 CL at 0 AoA, and a cruise weight of 2000 lb, it would need to be flying at 133 mph.
I get:
((.25-.053)/4.56)*(180/pi) = 2.475 degrees AoA.

This link appears to show that at 6 degrees AoA, the bottom surface produces roughly zero lift (due to the velocity averaging 1): http://www.mh-aerotools.de/airfoils/velocitydistributions.htm
There's signifcant area below the 1. I updated the picture with a line going across v=1:

velo6.gif

Cyrus
I'm not so sure. Here's the data for a 172: http://www.prism.gatech.edu/~gtg635r/Lift-Drag%20Ratio%20Optimization%20of%20Cessna%20172.html [Broken]

Here's a picture of the airfoil: http://www.windmission.dk/workshop/BasicBladeDesign/naca.html [Broken]

It's not flat on the bottom, it's curved, which means that at zero AoA the bottom surface has a negative contribution to the lift. By my calculation, with a .25 CL at 0 AoA, and a cruise weight of 2000 lb, it would need to be flying at 133 mph. Cruise speed for the 172 is 130mph. This is likely by design, as the minimum Cd tends to occur near 0 AoA.

Also: this link appears to show that at 6 degrees AoA, the bottom surface produces roughly zero lift (due to the velocity averaging 1): http://www.mh-aerotools.de/airfoils/velocitydistributions.htm

That data is a bit off. A 172 cruises at 105KTS ~120mph, NOT 120KTS.

At 120Kts, your 7kts away from the maximum structural crusing speed. Use a max weight of 2550lbs for your calculation.

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Cyrus
First of all, aircraft wings are usually fixed to the body at a slight positive angle. This is referred to as the wing's angle of attack. If you look at an aircraft sitting flat on the runway, with the cockpit facing left, you should be able to see this. The wing is actually turned clockwise a few degrees; the wing is pitched up, even when the aircraft body is flat. They do this because typical airfoil/wing geometries generate lift only when the wing sits at a positive angle of attack. Thus, by affixing the wing to the aircraft in this way, the aircraft will generate lift even when the body is sitting flat on the runway.

Now, imagine the aircraft on the runway again, with the cockpit facing to the left, as before. As the aircraft takes off, the airflow hits the wing, and "attaches" to it as it flows around it, assuming that the wing is properly designed and the flow remains laminar. Laminar flow basically just means that the airflow goes smoothly and continuously around the wing. From this, and considering how we just described the positive pitch of the wing, it's easy to see that the region of flow approaching the wing from the front turns downwards as it follows the shape of the wing. Hence, the top of the wing deflects the air downwards, but it's not like it's the top of the wing acting alone; it's really the entirety of the wing shape and geometric composition.

Careful, that's the angle of incidence. Not attack.

Homework Helper
Since I didn't edit the post in time, I'm reposting:

By my calculation, with a .25 CL at 0 AoA, and a cruise weight of 2000 lb, it would need to be flying at 133 mph.
Using the formula from that link I get:
((.25-.053)/4.56)*(180/pi) = 2.475 degrees AoA.

A NACA 2412 wing with no washout would need less AoA to produce the same CL. The article also states the washout backwards, as it's the tips that get a negative AoA relative to the root. I don't know what the root incidence is.

This link appears to show that at 6 degrees AoA, the bottom surface produces roughly zero lift (due to the velocity averaging 1): http://www.mh-aerotools.de/airfoils/velocitydistributions.htm
There's signifcant area below the 1. I updated the picture with a line going across v=1:

velo6.gif

At 2.475 degrees, there would be very little lift generated below the wing. I'm not sure how much increase in AoA would be required to cruise at a more reasonable (than sea level) 5000 feet.

Commercial airliners cruise at over 30,000 feet, and at a pretty significant AoA, although I haven't been able to find exact numbers.

Mentor
I get:
((.25-.053)/4.56)*(180/pi) = 2.475 degrees AoA.
What is that calculation? I'm using the lift equation to show how much lift you get at 0 AoA: Cl = Lift / ((1/2) * (rho) * ((velocity) ^ 2) * s)

.25=2000/(.5*rho*v^2*s)
.25=2000/(.5*.002377*v^2*175)
v^2= 196 fps = 134 mph

(I used a crusie weight of 2000lb, though Cyrus is saying I should use higher)
There's signifcant area below the 1. I updated the picture with a line going across v=1:

velo6.gif
You're right, I was thinking upside-down with that one.

Cyrus
To Russ: Your speed is too fast if your using 120kts. You have to use 105kts. (I would also use the density of air at 5000 feet, not sea level).

To Jeff: Angle of incidence at the root is what you have been mislabeling 'angle of attack'

http://www.centennialofflight.gov/essay/Dictionary/angle_of_incidence/DI6G1.jpg [Broken]

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Cyrus
What is that calculation? I'm using the lift equation to show how much lift you get at 0 AoA: Cl = Lift / ((1/2) * (rho) * ((velocity) ^ 2) * s)

.25=2000/(.5*rho*v^2*s)
.25=2000/(.5*.002377*v^2*175)
v^2= 196 fps = 134 mph

(I used a crusie weight of 2000lb, though Cyrus is saying I should use higher) You're right, I was thinking upside-down with that one.

Thats not going to be very accurate though. You are ignoring the fact that the fuselauge is creating lift, and that the tail is creating negative lift.

Homework Helper
Angle of incidence at the root is what you have been mislabeling 'angle of attack'.
I don't know what the incidence is, only that the article states that there is 3 degrees of wash-out, and the conflicted itself by stating incidence was -3 at the root and 0 at the tips, which would be wash-in, so this is wrong.

Mentor
Here's a link that discusses the issue and lists a plane with a 115kt cruise speed and a 4.5 degree AoA: http://www.av8n.com/how/htm/aoa.html

Note: this link uses the zero-lift definition of AoA, not the geometric definition. Using the previous link, the zero lift point is about -2 deg AoA for that wing, making the geometric AoA for the above link about 2.5 deg at cruise. Given cyrus's clarification of the performance, I'm willing to accept 2.5 deg instead of 0 for cruise.

Unfortunately all we've established is that somewhere above 0 deg and below 6 deg, the lower surface's contribution is 0, but some planes cruise with AoA's to the lower end of that.

In any case, we're getting a little specific about our scenario. The point that led to this little side argument just said that it was "common". I didn't specify cruise or max gross weight or anything. The point is that there are a lot of scenarios where a signficant amount of lift can be generated by the wing with no contribution by the lower surface.

Mentor
Thats not going to be very accurate though. You are ignoring the fact that the fuselauge is creating lift, and that the tail is creating negative lift.
We're getting too bogged down in specifics here anyway. All I was trying to accomplish with the last sentence in post 6 was to point out that there are lot of scenarios where the lower surface of a wing could contribute nothing to the lift generated by the wing.

Cyrus
I don't know what the incidence is, only that the article states that there is 3 degrees of wash-out, and the conflicted itself by stating incidence was -3 at the root and 0 at the tips, which would be wash-in, so this is wrong.

incidence is the angle the wing makes with the fuselage.

Cyrus
That's a misapplication of Bernoulli's principle to explain lift. This misapplication is unfortunately used quite widely. The attached diagram is simply incorrect. If the plane is to go up (or even stay level), something else must go down. That something else is air: The wings deflect air downward. Lift results from Newton's third law.

How the bottom side of the wing accomplishes this downward deflection is obvious. How the top of the wing contributes to this deflection at all is a lot less obvious. Moreover, in a good wing, it is the top rather than the bottom that does the bulk of the work in deflecting air downward. The link Jeff Reid posted does a nice job of explaining the Coanda effect.

He simply said overpressure and underpressure, not Bernoulli. In addition, this is correct. Lift is the integral of the pressure forces over the wing in the -z direction of an Earth fixed coordinate system (N.E.D. -North,East,Down).

$$L=Ncos(\alpha)-Asin(\alpha)$$

$$N'=-\int^{TE}_{LE}(p_u cos(\theta)+\tau_u sin(\theta)ds_u+\int^{TE}_{LE}(p_lcos(\theta)-\tau_l sin(\theta)ds_l$$

$$A'=-\int^{TE}_{LE}(-p_u sin(\theta)+\tau_u cos(\theta)ds_u+\int^{TE}_{LE}(p_l sin(\theta)+\tau_l cos(\theta)ds_l$$

You said the flow turns down. How do you think that happens? It causes an increase in pressure at the bottom of the wing.

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Stan Butchart
There are many foils with conditions that average zero pressure change below the wing. With this condition all of the FORCE that supports the wing comes from the ambient static pressure of the atmosphere. Pressure created by gravity. The objective for the flow above the wing is to reduce pressure force. There is no "pull".
I hope that someone can provide some meat for the implication that a downward deflection of air is required to give a lift force. For myself, while downflow is always the result of a passing wing, I cannot find a downflow within the "system" that is a reaction from any force that contibutes to the actual lift.

Cyrus
There are many foils with conditions that average zero pressure change below the wing. With this condition all of the FORCE that supports the wing comes from the ambient static pressure of the atmosphere. Pressure created by gravity. The objective for the flow above the wing is to reduce pressure force. There is no "pull".
I hope that someone can provide some meat for the implication that a downward deflection of air is required to give a lift force. For myself, while downflow is always the result of a passing wing, I cannot find a downflow within the "system" that is a reaction from any force that contibutes to the actual lift.

B1: Huh? Pressure created by gravity?

B2: Look at a control volume around the entire wing and use the Reyonlds Transport Theorem.

Stan Butchart
B1 -- The ambient prssure is derived from the force of gravity apon the mass of the atmosphere above.
B2 - Good this is the first hint that I have been given that such a relationship exists.
However you will have to help me out with Reyonlds Transport Theorem.

Homework Helper
All I was trying to accomplish with the last sentence in post 6 was to point out that there are lot of scenarios where the lower surface of a wing could contribute nothing to the lift generated by the wing.
Russ is correct, after more research, this is not as rare as I thought.

Most of my "research" about aerodynamics is due to one of my hobbies, flying radio control gliders. There has been a lot of airfoil design work done for rc glider contest models (F3B, F3J), mostly because more new rc glider models are released per year than full scale aircraft.

Anyway, I keep forgetting that most powered civilian aircraft cruise much faster than best lift to drag ratio speeds, unlike gliders, and at these faster speeds, the AoA is smaller and depending on the airfoil, there are cases where virtually no lift is generated by higher pressure below a wing.

Commercial airliners seem to use a higher AoA than say a twin engine civilian aircraft, probably due to a combination of a relatively heavy load (full passenger load for maximum profit), and high altitudes where jet engine thrust versus drag versus fuel consumed for distances traveled is optimum.

Homework Helper
I hope that someone can provide some meat for the implication that a downward deflection of air is required to give a lift force. For myself, while downflow is always the result of a passing wing, I cannot find a downflow within the "system" that is a reaction from any force that contibutes to the actual lift.

If there is a low pressure area above a wing, it causes air to accelerate towards it from all directions except upwards (and backwards) through the solid wing so the result is a net downwards (and forwards) acceleration of air. If there is a high pressure area below a wing, it causes air to accelerate away from it in all directions except upwards (and backwards) through the solid wing so the result also is a net downwards (and forwards) acceleration of air.

I refer to this link again:

"The physical cause of low or high pressure is the forced normal (perpendicular) acceleration of streaming air caused by obstacles or curved planes in combination with the Coanda-effect.":

http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html [Broken]

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Homework Helper
laminar airflow

A link to John Dreese's web site, parts 4 and 5 discuss how little air flow is laminar over many wings, and how "laminar" air foils increase laminar flow to 30% or more over the chord length of a wing.

In the case of gliders, laminar "bubbles" result in either more drag or less lift so the laminar air flow is deliberately broken up sooner than it normally would via rougher surfaces or turbulators (this is mentioned in the article).

http://www.dreesecode.com/primer/airfoil1.html

"The physical cause of low or high pressure is the forced normal (perpendicular) acceleration of streaming air caused by obstacles or curved planes in combination with the Coanda-effect.":

http://user.uni-frankfurt.de/~weltner/Mis6/mis6.html [Broken]
This is true for lift related effects, but drag related pressures and accelerations are in the direction of travel, not perpendicular to it. As a simple example, a bus traveling down a highway, or a wing at zero effective angle of attack produce no lift, but generate drag, air is accelerated forwards, and the pressure behind the bus or wing is lower than the pressure in front of the bus or wing.

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Holocene
That data is a bit off. A 172 cruises at 105KTS ~120mph, NOT 120KTS.

Really?

I fly a 172/S, and nearly always cruise at ~119KTS @ 2600RPM.

Cyrus
Really?

I fly a 172/S, and nearly always cruise at ~119KTS @ 2600RPM.

I fly a 172Q -180HP fixed propeller. Cruise speed is always 100-105KTS. What year is your airplane, and altitude you fly at?

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Holocene
I fly a 172Q -180HP fixed propeller. Cruise speed is always 100-105KTS.

Interesting. The 172/S is 180HP as well.

Although I must admit, 2600RPM is what Cessna defines as a "maximum" cruise.

"Normal" is 112KTS @ 2500RPM.

Holocene
I fly a 172Q -180HP fixed propeller. Cruise speed is always 100-105KTS. What year is your airplane, and altitude you fly at?

The plane is a 2001 (not mine though). On XC flights, typically 7,500', unless of course I'm headed in a more westerly dirrection. (Only a VFR pilot at the moment).

Cyrus
Yeah, my plane is from 83'. I am not that high either. Usually around 4,500 feet. That would explain why your going faster.

Holocene
You're lucky to have your own plane. I would love to be able to afford one.

Cyrus
You're lucky to have your own plane. I would love to be able to afford one.

Bahahah. Own my own airplane. -sorry, couldn't help it.

Homework Helper
Note: this link uses the zero-lift definition of AoA, not the geometric definition.
I prefer the term "effective angle of attack" since it means zero angle for zero lift, and is independent of the airfoil being used.

Given cyrus's clarification of the performance, I'm willing to accept 2.5 deg instead of 0 for cruise. The point is that there are a lot of scenarios where a signficant amount of lift can be generated by the wing with no contribution by the lower surface.
Which I've already posted that it was more common than I expected, since most of my knowledge on this stuff is glider oriented, where the speeds are near best lift to drag ratio, as opposed to the much faster cruise speeds of civilian aircraft.

I also mentioned the rare case where most of the lift is produced from under the airfoil with the m2-f2 type flying bodies.

Higher AoA becomes the norm for commercial airliners, because of their load factor (more passengers means more profit), and their high altitudes (best fuel milage with jet engines).